Engineering Chemistry S Datta

112 ENGINEERING CHEMISTRY
or
or
Again dx = k(a – x)3
dt
dx
( a – x) 3 = k dt
Integrating,
= kc 3 [when a – x = c]
= kc 2 (c – x) [when a = b ≠ c and (a – x) = c]
1 1
.
2
2 ( a– x)
= kt + z
(Integration constant)
When t = 0, x = 0
1
2
1 1
.
2
2 a
= Z ∴ Z =
1 1
–
2 2
( a – x)
2a
= kt
∴ kt = 1 2
L
N
M
L
N
M
1
2 2 a
1 1
–
2 2
( a – x)
a
∴ k = 1 1 1
–
2 2P = 1 x( 2 a – x)
2t ( a – x)
a t a ( a– x)
Characteristics of a Third Order Reaction
(i) Where x = 1 2 a,
F
HG
1 1
k = 1 a. 2a – a
2 2
.
2
t
2 F 1 I
2a
. a
2 K J
HG
I K J
O
Q
P
O
Q
2 2 2
2 1 2
a – a
1 4 1
= =
t 1 4
a
t
2
= 13 1
2
t 2
. a
or t = 1 3 1
2 2
k
. . a
= 3 1
.
2
2k
a
∴ t ∝ 1 2
a
So, the time required for the completion of the same fraction of the change is inversely
proportional to the square of the initial concentration.
(ii) k is dependent on the unit of concentration.
(iii) Unit of k is mole –1 sec –1 .
Examples of Third Order Reaction
(i) 2NO + O 2
⎯⎯→ 2NO 2
(ii) 2NO + Cl 2
⎯⎯→ 2 NOCl
(iii) SnCl 2
+ 2FeCl 3
⎯⎯→ SnCl 4
+ 2FeCl 2
Zero Order Reactions
There are certain reactions where rate of reaction does not diminish with time i.e., the
rate of the reaction is not dependent on the concentration of the reactant or, in other words,
rate of the reaction is proportional to the zero power of the concentration of the reactant i.e.,
3
4
1
2
a
a
2
4
.